14 questions linked to/from Motivation behind standard deviation?
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### probability variance formula intuition [duplicate]

Here is the formula for the variance : $\sigma^2=\dfrac{\sum(X-\mu)^2}{N}$. My question is why do we SQUARE the difference between the mean and the variable, why don't we use absolute value ...The ...
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### In calculating the standard deviation, why do we square the difference from the mean, as opposed to cubing? [duplicate]

This question has been bothering me for a while: In calculating the standard deviation, why do we square the difference from the mean, as opposed to cubing the differences (and then taking the cube ...
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### Why $\sqrt{\frac {\sum(x-\mu)^2} {N}}$ instead of $\frac {\sum{\Bigl|x-\mu\Bigr|}} {N}$? [duplicate]

Possible Duplicate: Motivation behind standard deviation? In statistics very often you see something of the sort: $$\textrm{quantity}=\sqrt{\frac {\sum(x-\mu)^2} {N}}$$ to measure things like ...
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### Why is variance defined this way? [duplicate]

I don't understand why $Var(X) = E((X-\mu)^2)$. It's defined as the "expected value of the square of the deviation of $X$ from the mean" but I don't understand why it couldn't be $E(X-\mu)$ as that ...
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### Where do the definitions in statistics come from? [duplicate]

The most statistics I ever took was a few lessons on it back in high school. What always bothered me is how arbitrary the definitions seemed. For instance, I remember having trouble with the ...
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### Why are squares chosen as a weighting method for quantifying the deviations from a mean?

Reading about variance and it occurred to me that this squaring business seems to be used many places in statistics. I think I understand that the square is used to help "weight" values which are ...
The common way to think about distance is Minkowski difference with the special case $r=2$. The definition for standard deviation is $\sqrt{\frac{1}{n-1} \sum (x_i - x)^2}$. Both of these definitions ...